Questions tagged [statistics]

Statistics is the study of the collection, organization, analysis, and interpretation of data.

58 questions with no upvoted or accepted answers
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1k views

Ensemble learning, multiple classifier system

I am trying to use a MCS (Multi classifier system) to do some better work on limited data i.e become more accurate. I am using K-means clustering at the moment but may choose to go with FCM (Fuzzy c-...
5
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0answers
180 views

Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function" $Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset $s \subset U$. One can see $Sig(t)$ as a stochastic process. ...
4
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0answers
119 views

Relative beat detection for two audio recordings

I'm trying to synchronize (overlap) two audio recordings of the same song: a complete HQ version, and an incomplete, noisy version (phone recording for example). The noisy recording may have had its ...
3
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0answers
2k views

4th order cumulant of signal

I'm trying to implement some code for watermarking on audio based on a scientific paper. I'm stuck in the part of the pseudo code where they calculate the fourth order cumulant of the approximation ...
2
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0answers
40 views

Estimating shot noise - what's the origin?

If I have some photon detector, say a CCD, how do I estimate the error introduced by shot noise correctly? Typically, sources found on the internet say that the shot noise is the square root of the ...
2
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0answers
83 views

What is the physical significance of statistical quantities like mean, variance, skewness and kurtosis of a digital signal?

I understood the mathematical meanings of the mean, variance, skewness and kurtosis. But when we calculate these quantities for a signal (say a digital audio signal), what physical meaning do they ...
2
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0answers
32 views

Finding the error in the total integrated intensity of a fitted 2D Gaussian

I have been trying to fit signals to a 2D Gaussian function, and while I have bene able to use sciKit-image's curve_fit function to find the covariance matrix for ...
2
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0answers
30 views

how to robustly estimate low and up envelope of signal with trend, few level constant steps and noise

I am looking for robust estimation method of low and up envelope of the signal consisting from smooth trend component, constant steps between few fixed levels and additive noise (+ outliers of course)....
2
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0answers
45 views

Is there any method/algorithm to estimate the magnitude of non-stationarity in a signal?

e.g. the global Lyapunov exponent can give sense of the level of chaos in the signal. Is there any reliable numerical technique to estimate "how" non-stationary (or how predictable) a signal is? Also, ...
2
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0answers
88 views

Obtaining n values from n-1 sensors

As the questions states, lets consider we have 3 gas sensors giving me data for: A B C Note that only sensors for A and B give absolute values, yet we need the absolute values for all four species:...
2
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0answers
219 views

Distribution of a signal covariance matrix

A common estimation problem in signal processing assumes the following signal model \begin{equation} \mathbf{r} = \sum_{i=1}^{Q}\alpha_i\mathbf{s}\left(w_i\right)+\mathbf{n} \end{equation} where $\...
2
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0answers
65 views

Predicting Positional Displacement with a Bivariate Gaussian Distribution

In my computer-vision problem, a blob can move either forward or backwards (with a slight chance of moving sideways) along its directional axis. I am seeking a bivariate model because I need to ...
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0answers
17 views

Linearity of the system with Pearson correlation sliding window

I have a sampling system that consists of linear and non-linear components(analog filters, ADC, CPU, and so on). I made some HW changes and I want to verify that the linearity was preserved. My method:...
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0answers
61 views

Fisher Information Matrix for sinusoidal signal under multiplicative noise

Consider observations ($y$) of a sinusoidal wave with multiplicative noise ($v$) where we are estimating unknown frequency ($\omega$) and unknown initial phase ($\theta$). We can write this system ...
1
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0answers
50 views

Short Time Fourier Transform has different frequencies than Fourier Transform?

The reason we do the STFT is so that we can analyse for short segments of time how much of the components in the frequencies of the FT are present. However, it may be possible that completely ...
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0answers
24 views

ICA School Project

I have been stuck on my school project that consists of independent component analysis. My code will run, but only 50-60% of the time it unmixes the signals. Another problem I have is the amplitudes ...
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0answers
16 views

How do I show that two sets of spectra are different?

I essentially have 6 spectral curves, 3 repeats for two samples. I want to be able to show that two samples are distinct (if they are). I have tried spearman's correlation already, which does produce ...
1
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1answer
102 views

An Interesting Model with Unknown Orthogonal Design Matrix

Suppose the multivariate one-way anova model for the raw data , i.e. $$ \label{Example_model_1} \mathbf{y}_{ij}=\mathbf{\mu}+\mathbf{z}_i+\mathbf{e}_{ij}, ~~ i=1,\ldots,m,~~j=1,\ldots,n_i,~~~~~~~~~~...
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0answers
109 views

Threshold for CAF Surface

I am calculating a time partitioned Cross Ambiguity Function (CAF) by adding the surfaces of different time-sectioned CAFs together. Meaning, I calculate a CAF using 10 seconds of IQ data, calculate a ...
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0answers
491 views

Estimate standard deviation of random-walk using Kalman filter

I'm new to Kalman filters so this might be a stupid question. I created a Kalman filter that takes in time series observations and estimates the mean of that time series. This is simply modeling a ...
1
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0answers
627 views

How to detect overall error between two signals and also track changes occurred

I need to develop an algorithm that will compare two signals (1 Reference Signal and other is measured signal values from sensor) and generate some metric(s) to describe changes between them. I am not ...
1
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0answers
53 views

Variance and Co-variance of a Linear Forecast

Consider a linear forecasting problem where all shocks $\{\epsilon_i\}_1^n$ are independently distributed with $\epsilon_i\sim N(0,\sigma_i^2)$ for all $i$. Suppose you want to forecast $\theta = \...
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0answers
42 views

variance of filtered polynomial

Consider the following system: What is the variance of $y$, $\mathbb{E}(y^2)$ ? (EDIT: I know input signal has infinite power but will be made bandlimited by $H$. Both $H$ and $G$ are simple ...
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0answers
105 views

Received signal envelope PDF to power PDF [Wireless Communications]

I am deriving the probability density function (pdf) of the received wireless signal envelope in multi-path fading channels. I wish to transform this envelop PDF to the power PDF of that signal. I ...
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0answers
54 views

Pearson correlation of neural responses with it's linear estimation

I am trying to understand the following fact from this article (page 13): How can single neurons predict behaviour Suppose I have a linear estimation of a stimulus: $ \hat{s} = \mathbf{w}^T(\mathbf{r}...
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37 views

How can a medical doctor use the information given by someone working in medical image computing(shape analysis)? Details follow

Posted also here, where it's been put on hold. I did modify it afterwards though. https://biology.stackexchange.com/questions/43997/how-can-a-medical-doctor-use-the-information-given-by-someone-...
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0answers
468 views

Are discrete wavelet transform based statistical features invariant to rotation/translation/scale?

I'm reading a paper where image classification is done. Their approach is to use the discrete wavelet transform with bi-orthogonal wavelets of degree 3.5 and decomposition of level 3 on images. Based ...
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0answers
182 views

The autocorrelation of a WSS process as a linear operator

If I'm given a autocorrelation matrix of a WSS process what interpretation should I put on the resulting vector. More concretely the matrix takes the form $\begin{bmatrix} x_1 & x_2 & \...
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0answers
70 views

Solving an Array Signal Processing Estimation Problem based on the Rayleigh Quotient

The Rayleigh quotient for a covariance matrix $\mathbf{C}$ and a non-zero steering vector $\mathbf{a}$ is given by $$ R(\mathbf{C},\mathbf{a}) := \frac{\mathbf{a}^H\mathbf{C}\mathbf{a}}{\mathbf{a}^H\...
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0answers
35 views

Statistics of the output of a high bitrate signal filtered through a narrow band low pass filter

I was wondering what would be the statistics of the output of the filtering of an extremely wideband signal (e.g. 10 Gbps random data stream) through a narrowband low-pass filter (e.g. 10 MHz LP). I ...
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0answers
227 views

Yet Another Peak Detection Request

I looked over the other entries regarding peak detection and none seem to answer my question. I'm working with Fourier spectra of digitized audio that can't be measured again. There are no ...
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0answers
199 views

Random signal modeling with Matlab

I want to build a detector of sorts. Say I have a bunch of signals and they all share some patterns, like some peaks in frequency or something more complicated that I can't bother to calculate by hand....
0
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0answers
21 views

How to handle skewness and kurtosis parameters of missing data?

I'm working on acoustic signal classifier. Most signals are characterized by having two echoes (peaks). Each echo can be described by maximum value, duration, skewness and kurtosis. Thus each signal ...
0
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0answers
11 views

How to use numpy covariance result to get a correction factor and make my second signal to exactly overlap on my first signal?

covariance = np.cov(y1_interp, y2_interp)[0][1] print('covariance is', covariance) covariance is 0.00010861874695023591 This number shows how different my signal 2 ...
0
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0answers
69 views

Dividing a data set into segments with consistent inner behavior, using segmentation algorithms and metrics for consistency

Context of the problem: I have signal data which was recorded in a software system and which shows the runtime of multiple processes over time. In total there are more than 900 processes each having ...
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0answers
46 views

Is sum of squares of normally distributed Random variables follow Chi square distribution?

Actually standardized variable z of x(which has a normal distrbution) is (x - E(x))/squareroot(E(x-E(x)) ^ 2) In chi-square distribution we have that sum of squares of unit normal distribution ...
0
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0answers
22 views

Determination of Variance from Symbol Error Probability Equation

For a M-ary QAM receiver, the symbol with AWGN noise is received and detected with Maximum–Likelihood (ML) Decision algorithm. The symbol error probability (SEP)is approximated as : here, Eb is the ...
0
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0answers
18 views

How can we interpret Spatial Cross Correlation between two images in case of compressed sensing based reconstruction of images?

I am reconstructing images using compressed sensing. The images are used from sipi database. One particular image, named Female Bell Lab, which is giving better result with high PSNR around 42 dB and ...
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0answers
15 views

What are some good references that define images from a statistical point of view?

I know that images can be studied and understood as 2 dimensional signals. However, I hope you can point me towards references that define and present images rigorously in terms of realisations of a ...
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0answers
161 views

Trying to implement matlab pwelch function in python using scipy welch

I am trying to port the statistics toolbox function pwelch from matlab into python, but when I am trying to implement it using scipy.signals.welch, it does not return the same results as it does in ...
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0answers
20 views

Unable to interpret hypothesis testing whetehr a signal is periodic or not

The meaning of P value is probability which should be number between 0 (the event never occurs) and 1 (the event occurs always). significance testing for periodicity using Matlab gives a documentation ...
0
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0answers
37 views

Choose the right Sigma for Gaussian filter

I have the following problem: I have a time series with counted data. I now want to smooth it using a Gaussian low-pass filter. Is there a method to determine the sigma value? The window should have a ...
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0answers
14 views

Calculate ACF in C++?

I would like to manually reproduce the method that authors of an article used in their research (DOI: 10.1038/s41598-017-02750-9 (Page 8. top)). It is mentioned as "ACF", so I wrote ...
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0answers
27 views

When is Markov a Martingale

I have two questions and I am very confused about the concepts Can a Markov process of order one also be a a Martingale? Is any Markov process of order one also a Martingale? For 1. I would say yes, ...
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0answers
31 views

Generating data with given Auto and Cross Correlations

I have two discrete vectors $\mathbf{x}_1$ and $\mathbf{x}_2$, and I'm trying to generate more data $\mathbf{f}_1$ and $\mathbf{f}_2$ that has some basics properties of $\mathbf{x}_1$ and $\mathbf{x}...
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0answers
30 views

standard deviation of two constant noised signals related through interpolation

Let us say say we have a noised constant signal and want to evaluate the standard deviation (std) of the noise. We calculate the std of the said noised signal and call it $\sigma_1$. Now we process ...
0
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1answer
77 views

Lower bound of weighted average of sequence

Can anyone prove that $$\mathrm{avg}\left(\frac {a_i}{\left(1+a_i\right)^2}\right) \ge \frac{\mathrm {avg}({a_i})}{\left(1+\mathrm{avg}{(a_i)}\right)^2}$$ for a sequence of positive valued elements $...
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0answers
39 views

About convergence of KL divergence: if the two probability distributions are type, does the law of large number work?

If I pick $N$ samples from $P_X$ and $P_Y$, they are two independent discrete distributions. $X_1,X_2,\ldots,X_N$ are drawn i.i.d from $P_X$, and $Y_1,\ldots,Y_N$ are drawn i.i.d from $P_Y$. I got $...
0
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1answer
80 views

Generalized Likelihood Ratio test for correlated data

Consider a sequence of random variables $\overline{z} = \{z(k-M+1), ..., z(k)\}$, with probability density depending upon a scalar parameter $\theta$. It is intended to decide between two hypotheses ...
0
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0answers
34 views

CWT coefficients as features for ML algorithms

I use CWT coefficients as features in ML algorithms and then I did the feature selection using the chi-square test but recently I figured out that the chi-square test can only be applied for ...